Abstract
We present a measurement of the Michel parameters of the $\tau$ lepton, $\bar{\eta}$ and $\xi\kappa$, in the radiative leptonic decay $\tau^- \rightarrow \ell^- \nu_{\tau} \bar{\nu}_{\ell} \gamma$ using 711~f$\mathrm{b}^{-1}$ of collision data collected with the Belle detector at the KEKB $e^+e^-$ collider. The Michel parameters are measured in an unbinned maximum likelihood fit to the kinematic distribution of $e^+e^-\rightarrow\tau^+\tau^-\rightarrow (\pi^+\pi^0 \bar{\nu}_\tau)(\ell^-\nu_{\tau}\bar{\nu}_{\ell}\gamma)$ $(\ell=e$ or $\mu)$. The measured values of the Michel parameters are $\bar{\eta} = -1.3 \pm 1.5 \pm 0.8$ and $\xi\kappa = 0.5 \pm 0.4 \pm 0.2$, where the first error is statistical and the second is systematic. This is the first measurement of these parameters. These results are consistent with the Standard Model predictions within their uncertainties and constrain the coupling constants of the generalized weak interaction.
Highlights
In the Standard Model (SM), there are three flavors of charged leptons: e, μ, and τ
The SM has proven to be the fundamental theory in describing the physics of particles; precision tests may reveal the presence of physics beyond the Standard Model (BSM)
According to Ref. [9], ξ κ is related to another Michel-like parameter ξ = −ξ − 4ξ κ + 8ξ δ/3
Summary
In the Standard Model (SM), there are three flavors of charged leptons: e, μ, and τ. The SM has proven to be the fundamental theory in describing the physics of particles; precision tests may reveal the presence of physics beyond the Standard Model (BSM). I,j=L,R where GF is the chirality the Fermi indices of constant, i and the neutrinos, j are is e the chirality indices for the or μ, S = 1, V = γ μ, charged T =i γ leptons, μγ ν − γ n and νγ μ m √are /2 2 are, respectively, the scalar, vector, and tensor Lorentz structures in terms of the Dirac matrices γ μ, ui and vi are the four-component spinors of a particle and an antiparticle, respectively, and giNj are the corresponding dimensionless couplings. In the SM, τ − decays into ντ and a W −-boson, the latter (a) (b)
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